President Obama and Scott Walker / MANDEL NGAN, AFP/Getty Images

by David Jackson, USA TODAY

by David Jackson, USA TODAY

President Obama shook hands and chatted with his one of his most outspoken Republican critics, Wisconsin Gov. Scott Walker -- but he won't be meeting with the Democrat seeking to oust Walker in the November election, businesswoman Mary Burke.

"Mary Burke has a full day scheduled in western Wisconsin Thursday and will not be able to join the president during his visit to Wisconsin," Burke spokesman Joe Zepecki told the Milwaukee Journal Sentinel.

State Republicans were quick to say that Burke sees Obama as a political liability, a suggestion the Democrats denied.

Joe Fadness, the executive director of the state Republican Party, told the Journal Sentinel: "It's no surprise that millionaire Mary Burke is hiding from President Obama, her party's unpopular leader and the architect of a disastrous health care law and policies that have resulted in record debt and a sluggish national economy."

Zepecki did say that Burke spoke with Obama by phone on Wednesday, the Journal Sentinel reported.

For his part, Walker told reporters: "I don't know about Mary, but for me, I'm the governor, so whether I agree or disagree with everything he's done or is doing as president, it's important for me on behalf of all the people of the state of Wisconsin to officially greet the president, to thank him for his presence here."

Obama is speaking Thursday at a General Electric facility in Waukesha, Wisc.

During an appearance earlier this month in North Carolina, another prominent Democratic candidate -- incumbent Sen. Kay Hagan, facing a tough re-election bid -- also did not appear with Obama.

White House spokesman Jay Carney said the president is focused on "an agenda designed to expand opportunity" for all Americans.

"That's an agenda that should be welcomed by Americans across the country regardless of how they vote, their political affiliation," Carney said.

He added that Obama "obviously supports Democratic candidates, both incumbents and challengers across the country, and I think we've amply demonstrated that support already and he will continue to do so."